In FC-HBF, as shown in Fig. REF (a), each RF chain is connected to all \(N_{\sf {T}}\)  antennas through PS and combiners. Considering that the PS are quantized on \(q\)  bits, the set of feasible AP has size \(2^{q N_{\sf {T}} N_{\sf {RF}}}\) . Conventional HBF solutions either consider a codebook-based solution to limit the set of feasible solutions [1]} or use real-valued PS [2]}, which is not practical in a realistic system. The conventional approach consists in first designing the optimal FDP matrix, denoted \(\mathbf {U}_{\sf {opt}}=[\mathbf {u}_{1}, ..., \mathbf {u}_{u}, ..., \mathbf {u}_{N_{\sf {U}}}]\) , where \(N_{\sf {RF}} = N_{\sf {T}}\) . Then, the AP and DP are designed in such a way that the resulting precoder approximates \(\mathbf {U}_{\sf {opt}}\)  as follows:
\(\underset{\mathbf {A}_{q}, \mathbf {w}_{u}}{\operatornamewithlimits{minimize}} \big \Vert \mathbf {U}_{\sf {opt}} - \mathbf {A}_{q} \mathbf {w}_{u}\big \Vert ^2 \hspace{22.76219pt}\text{s.t. (\ref {cnt2})}, \) 
